Volume 20, pp. 212-234, 2005.

Abstract

This paper presents an alternative approach to the solution of diffusion problems in
the variable-coefficient case that leads to a new numerical method, called a Krylov
subspace spectral method.
The
basic idea behind the method is to use Gaussian quadrature in the spectral
domain to compute components of the solution, rather than in the spatial domain as
in traditional spectral methods. For each component, a different approximation of the solution
operator by a restriction to a low-dimensional Krylov subspace is employed, and each
approximation is optimal in some sense for computing the corresponding component.
This strategy allows accurate resolution of all desired frequency components without
having to resort to smoothing techniques to ensure stability.